What is (\partial)/(\partial x)((x^{1-a})/(1-a)) ?

The answer to (\partial)/(\partial x)((x^{1-a})/(1-a)) is x^{-a}

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(\partial)/(\partial x)((x^{1-a})/(1-a))

\frac{\partial}{\partial x} (\frac{x ^{1 - a}}{1 - a})

x^{- a}

Solution steps

\frac{\partial}{\partial x} (\frac{x ^{1 - a}}{1 - a})

Take the constant out:

(a \cdot f)^{'} = a \cdot f^{'}

= \frac{1}{1 - a} \frac{\partial}{\partial x} (x^{1 - a})

Apply the Power Rule:

\frac{d}{d x} (x^{a}) = a \cdot x^{a - 1}

= \frac{1}{1 - a} (1 - a) x^{1 - a - 1}

Simplify

\frac{1}{1 - a} (1 - a) x^{1 - a - 1} : x^{- a}

= x^{- a}

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What is (\partial)/(\partial x)((x^{1-a})/(1-a)) ?
The answer to (\partial)/(\partial x)((x^{1-a})/(1-a)) is x^{-a}